80 yd. Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house s at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk hrough the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90 ^ - angles. how much shorter is it for Sylvia to walk through the park? (1 point) Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be 60 X vards shorter.
If Sylvia walks straight down Johnson Avenue and then turns right on 41st Street, the total distance she will walk is the sum of the distance from her house to the intersection (42nd Street to 41st Street, which is 80 yards) and the distance along 41st Street to the bank (60 yards).
So the total distance she will walk is 80 + 60 = 140 yards.
If Sylvia walks through the park, she can take a shortcut directly from the intersection of 42nd Street and Johnson Avenue to the intersection of 41st Street and Edison Avenue.
Using the Pythagorean theorem, the diagonal distance is the square root of the sum of the squares of the two shorter sides. The shorter sides are 80 yards and 60 yards.
So the diagonal distance (the shortcut through the park) is sqrt(80^2 + 60^2) = sqrt(6400 + 3600) = sqrt(10000) = 100 yards.
Therefore, the shortcut through the park is 140 - 100 = 40 yards shorter than walking straight down Johnson Avenue and 41st Street.